Ph.D. in Cosmology and General Relativity at Queen's University at Kingston, Canada (2002).

Research Associate in Cosmology at Princeton University, New Jersey, USA (2002-2005).

Professor at the University of Texas at Dallas, USA (2005-present).

For my Curriculum Vitae (February 2020) click here.

For a picture gallery of random pictures of my family (outdated!): click here.

2018-2019 Invited review article in Living Reviews in Relativity journal to cover the topic of "Testing General Relativity at Cosmological Scales."
Living Reviews in Relativity 22 (2019) 1-204. arXiv:1806.10122.

2018 Award for Outstanding Teacher of the Year from the School of Natural Sciences and Mathematics.
University of Texas at Dallas

2013 Robert S. Hyer Award for Excellence in Research from the Texas Section of the American Physics Society. Jointly with Michael Troxel.

Journal paper highlighted at Physical Review Letters as Editors' suggestion and selected for a synopsis in *Spotlighting Exceptional Research in Physics* website of the American Physical Society. "Stringent Restriction from the Growth of Large-Scale Structure on Apparent Acceleration in Inhomogeneous Cosmological Models",
Mustapha Ishak, Austin Peel, and M. A. Troxel. Phys. Rev. Lett. 111, 251302 (2013).

2007 Award for Outstanding Teacher of the Year from the School of Natural Sciences and Mathematics.
University of Texas at Dallas

Journal paper selected by Chief Editor Gerardus 't Hooft (Nobel Laureate in Physics 1999)
to appear in the highlights of 2008 of the Foundation of Physics Journal. Article title: Remarks on the
formulation of the cosmological constant/dark energy questions. Mustapha Ishak. Foundation of
physics Journal, 37:1470-1498,2007.

Journal Paper voted by the Editorial Board of Classical and Quantum Gravity
Journal as one of the journal's highlights of 2002. Article title: Interactive
Geometric Database, Including Exact Solutions of Einstein's Field Equations,
Mustapha Ishak and Kayll Lake, Classical and Quantum Gravity 19, 505 (2002).

2002-2004 Postdoctoral Fellowship for Excellence in Research and Leadership from the
Natural Sciences and Engineering Research Council of Canada (NSERC)

I am a theoretical astrophysicist. My recent research projects and interests are in Physical Cosmology, Gravitational Lensing, and General Relativity (see next section).
I am involved in theoretical, numerical, and data-related projects. I am a full member of
the LSST Dark Energy Science Collaboration (DESC) working mainly within the Theory-Joint-Probes (TJP) and the Weak Lensing (WL) groups.

I completed my Ph.D. in 2002 in Cosmology and General Relativity with Prof. Kayll Lake at the Physics Department at Queen's
University at Kingston in Canada. My graduate work included investigations in inhomogeneous cosmological
models; an inverse approach to Einstein's equations; oscillation modes in compact astrophysical objects;
and matching spacetimes using junction conditions.

Then, I joined the Physics Department at Princeton University as a postdoctoral fellow where I worked
on projects in cosmology, cosmic acceleration and gravitational lensing with Prof. Steinhardt, Prof. Seljak and other
researchers. After that, I worked as a Research Associate at the Astrophysical
Sciences Department at Princeton in collaboration with Prof. Spergel and other researchers on cosmic acceleration and testing gravity at cosmological scales.
While there, I organized the Princeton & IAS Gravitational Lensing Seminar and taught (preceptor with lecturer appointments) at the Physics Department (Physics 103) and the Astrophysics Department
(Astro 203).

In 2005, I started a professorship position at the Department of Physics at the University of Texas at
Dallas (UT Dallas). I discovered that a real thirst for Cosmology and Astrophysics
exists within the students at UT Dallas and also the general public in the Dallas
Metroplex Area, so I launched a number of initiatives
and activities in response to that. I formed the new Cosmology, Astrophysics and Relativity Group at UT Dallas.

For a partial list of my papers at NASA ADS server
click here.

For a partial list of my papers at INSPIRE HEP server
click here.

With students, we developped a software package called ISiTGR (Integrated Software in Testing General Relativity) that is an
integrated set of modified modules for the software package CosmoMC for use in testing whether observational data is
consistent with general relativity on cosmological scales.
Click here for ISiTGR webpage.

I very much enjoy classroom teaching and mentoring students. The courses I taught at UT-Dallas include PHYS2325 Mechanics,
PHYS3312 Classical Mechanics, PHYS4V89 Cosmology, PHYS5303 Math Methods for Physics III (Graduate Course), PHYS5395 Cosmology (Graduate Course),
PHYS5311 Classical Mechanics (Graduate Course), PHYS5391 Special Relativity (Graduate Course), and PHYS5392 General Relativity (Graduate Course).
I received the 2007 Outstanding Teaching Award from the School of Natural Sciences and Mathematics at UTD.
For a detailed list of my course teaching
click here.

My research work received funding from NASA, DOE, NSF, private foundations and corporate sector.

I served as proposal reviewer for NSF, NASA, the Research Foundation of Canada, CONICYT Chile, The Foundation of Polish Science, and the Texas Space Grant Consortium. I served as referee for Physical Review Letters, Physical Review D, Astronomy & Astrophysics, Classical and Quantum Gravity, Monthly Notices of Royal Astronomy Society, General Relativity and Gravitation, Euro-Physics Letters and Physics Letters B. I have been member of UTDallas senate for 9 years and participated or chaired over 10 university or school committees. I chaired (jointly with Prof. Wolfgang Rindler) the local and scientific organizing committees of the 27th Texas Symposium on Relativistic Astrophysics. The symposium received 470 participants, over 300 talks in 49 parallel sessions; 24 plenary and review talks, and a public lecture attended by over 1300 people. More info and the online proceedings are available at http://nsm.utdallas.edu/texas2013. I organize and look after the activities and expansions of the new Cosmology, Astrophysics and Relativity Group at UT Dallas.

Mustapha Ishak - Kayll W. Lake - Robert C. Roeder - George C. McVittie - Arthur S. Eddington

(Credit for reconstructing this genealogy goes to Prof. Kayll Lake)

- The origin/cause of the acceleration of the expansion of the Universe: Cosmological Constant, Dark Energy, Extensions to General Relativity.
- Testing Dark Energy versus Modified Gravity at Cosmological Scales of Distance. Software we developped for this..
- Gravitational Lensing and applications to cosmology. Intrinsic Alignments of Galaxies.
- Constraining cosmological parameters and cosmological models using probes such as gravitational lensing, the cosmic microwave background (CMB), and supernova searches.
- Inhomogeneous Cosmological Models and the averaging problem in cosmology
- Selected topics in General Relativity and Exact Solutions to Einstein's Equations
- Projects at the intersection of modern cosmology and General Relativity
- Junction conditions for matching spacetimes and constructing wormholes and thin-shells
- Computer Algebra (symbolic computing) and application to cosmology and general relativity

Exact Solutions to Einstein's Equations In Astrophysics. Plenary talk given at the Texas Symposium in Relativistic Astrophysics in Geneva (2015).

Two Big Puzzles in Modern Cosmology. Public lecture given at Southern Methodist University (SMU) in Dallas (2015).

Constraints and tensions in Modified Gravity Parameters from Planck, CFHTLens and other data sets including Intrinsic Alignemnets Systematics. Invited talk presented at Testing Gravity Conference at Simon Fraser University (2015).

Why is the Expansion of the Universe Accelerating? Plenary talk given at the Texas Sections of the American Physical Society. Texas A&M at Commerce (2011).

Constraints from Cosmological Data on Expansion and Growth of Structure in a Macroscopic Gravity Averaged Universe. Contributed talk given at the American Astronomical Society Meeting in San Diego (2016).

**Graduated Ph.D. Students:**

1. James Richardson (graduated in May 2008). Working in the corporate sector

2. Jacob Moldenhaeur (graduated in May 2010). Assistant Professor and Acting Chair at Physics Department, University of Dallas, TX.

3. Anthony Nwankwo (graduated in May 2011). Working in the corporate sector.

4. Jason Dossett (graduated in May 2013). Research staff member at the Institute for Defense Analyses, Washington, DC

5. Michael Troxel (graduated in May 2014). Assistant Professor of Physics, Duke University.

6. Austin Peel (graduated in May 2015). Postdoctoral Research Position in Astrophysics at Laboratoire d'Astrophysique, Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland.

7. Tharake Wijenayake (graduated in May 2016). Working as Senior Analyst in the corporate sector at Zackâ€™s Investment, Chicago, IL.

8. Ji Yao (graduated in May 2018). Working as postdoctoral research fellow at Shanghai Jiao Tong University.

9. Weikang Lin (graduated in August 2018). Working as postdoctoral research fellow at North Carolina State University.

** Current Ph.D. students: **

1. Eske Pederson (graduation expected in 2021).

2. Anish Agash (graduation expected in 2021).

3. Cristhian Garcia Quintero (graduation expected in 2024).

4. Leonel Medina Varela (graduation expected in 2026)

**Masters students supervised**

1. Chris Allison

2. Jeffrey Scott

3. Brian Troup

4. Delilah Whittington

5. John Thompson

6. Lee Caps

Mustapha Ishak and former graduate students Jason Dossett, Austin Peel and

Michael Troxel at the 219th AAS Annual Meeting, Austin, TX (2012)

1. Katherine Morgan (undergraduate Thesis/research, 2006)

2. Lee Isaac Trawick, (undergraduate Thesis/research, 2006)

3. Sriram Nagaraj, (undergraduate Thesis/research, 2006)

4. Wendy Gartenberg, (undergraduate Thesis/research, 2007)

5. John Wilson (undergraduate Thesis/research, 2007)

6. Jason Dossett, (undergraduate Thesis/research, 2007, 2008)

7. Tan Lee, (undergraduate Thesis/research, 2008)

8. Austin Peel (undergraduate Thesis/research, 2007)

9. John Thompson (undergraduate Thesis/Research, 2008)

10. Lee Caps ((undergraduate Thesis/research, 20010)

11. Thomas Griffins (Undergraduate Research Project, 2012)

12. Nathan Newton (Undergraduate Research Project, 2012)

13. Jonathan Woodbury (undergraduate Thesis/research, 2013)

14. Victor Lee (Undergraduate Research Project, 2015)

15. Joseph Burnett (Undergraduate Thesis/Research, 2015)

16. Cristhian Quintero (Undergraduate research, 2016)

17. Logan Fox (undergraduate research, Spring and Fall 2017)

18. Lindsey Rayborn (undergraduate research, Spring and Fall 2016)

19. Leonel Medina (undergraduate research, 2018)

20. Aaron Boggs (REU undergraduate research, 2019).

21. Calvin Ross (undergraduate research, 2019-2020).

On the picture above: Mustapha Ishak with undergraduate students Jonathan Cohen, Corinne

Blangy, Parikshit Krishnia, Alex Riley, and Brian Baragas after a discussion about the

science of the Movie the Martian (nominated for 4 Oscars). Did they get the science right?

Gravitational Lens: Galaxy Cluster 0024+1654

W. N. Colley, E. Turner (Princeton University), J. A. Tyson (AT&T Bell Labs), and NASA

1. Tim Carlton summer 2006

2. Ray Whitside, summer 2007

3. Sid Mittal, summer 2008

4. Parker Maginley, summer 2008

5. Brandyn Lee, summer 2009

6. Scott Meesse, summer 2009

7. Genway Huang, summer 2010

8. Evan Remmele, summer 2011

9. Amelia Neild, summer 2018

10. Emily Bailey, summer 2018

"Cosmological discordances: a new measure, marginalization effects, and application to geometry vs growth current data sets". Weikang Lin, Mustapha Ishak. Physical Review D 96, 023532 (2017).

"Cosmological discordances. II. Hubble constant, Planck and large-scale structure data sets." Weikang Lin, Mustapha Ishak Physical Review D 96, 083532 (2017).

Article by UT-Dallas News Services about the work: "Stringent Restriction from the Growth of Large-Scale Structure on Apparent Acceleration in Inhomogeneous Cosmological Models. , Mustapha Ishak, Austin Peel, M.A. Troxel, published in Physical Review Letters 111, (2013) 251302. (http://arxiv.org/abs/1307.0723). Paper was also highlighted at Physical Review Letters as Editors' suggestion and selected for a synopsis in

Press release article that appeared in Astronomy Magazine, Spaceflight Now and NASA's Beyond Einstein website, about the work: "Probing Cosmic Acceleration Beyond the Equation of State: Distinguishing between Dark Energy and Modified Gravity Models. Mustapha Ishak, Amol Upadhye, David N. Spergel (2005). astro-ph/0507184. Physical Review D, 74, 043513 (2006)."

Faculty highlight article by UT-Dallas media services (2008).

PI, PI, Department of Energy, 2018-2021 (Project in Cosmology and Dark Energy)

PI, National Science Foundation, 2018-2019 (Project in Gravitational Lensing)

PI, National Science Foundation, 2015-2018 (Project in Astrophysics and Gravitational Lensing)

PI, The John Templeton Foundation, 2014-2017 (Research Project in Cosmology)

PI, National Science Foundation, 2011-2014 (Research Project in Astrophysics and Gravitational Lensing)

PI, Department Of Energy, 2010-2013 (Research Project in Cosmology and Dark Energy)

PI, NASA Astrophysics Theory Program, 2009-2012 (Research Project in Cosmology and Cosmic Acceleration)

PI, Texas Space Grant Consortium, to start in 2008 (Research Project in Astrophysics and Cosmic Acceleration)

PI, From Corporate Sector, 2008 (Research Project I in Gravity & statistics)

PI, From Corporate Sector, 2009 (Research Project II in Gravity & statistics)

PI, Hoblitzelle foundation, 2006 (Grant to build a Computer Cluster)

, Tharake Wijenayake, Weikang Lin, and Mustapha Ishak. Published in*" Averaged universe confronted with cosmological observations: A fully covariant approach. "***Physical Review D**94, 083501 (2016) Paper available at https://arxiv.org/abs/1604.03503.

, M.A. Troxel, Mustapha Ishak. Invited Review Published in*" The Intrinsic Alignment of Galaxies and its Impact on Weak Gravitational Lensing in an Era of Precision Cosmology. "***Physics Reports**558, 1-59, (2015): doi:10.1016/j.physrep.2014.11.001 (2014). Paper available at http://arxiv.org/abs/1407.6990.

, Jason N. Dossett, Mustapha Ishak, David Parkinson, Tamara M. Davis. Published in*" Constraints and tensions in testing general relativity from Planck and CFHTLenS including intrinsic alignment systematic. "***Physical Review D**92, 023003 (2015) Paper available at http://arxiv.org/abs/1501.03119.

, 3. Tharake Wijenayake, Mustapha Ishak. Published in*" Expansion and Growth of Structure Observables in a Macroscopic Gravity Averaged Universe "***Physical Review D**91, 063534, (2015) Paper available at http://arxiv.org/abs/1503.05796.

, M. A. Troxel, Mustapha Ishak Published in*" Cross-correlation between cosmic microwave background lensing and galaxy intrinsic alignment as a contaminant to gravitational lensing cross-correlated probes of the universe "***Physical Review D**89, (2014) 063528. Paper available at http://arxiv.org/abs/1401.7051.

, Austin Peel, M. A. Troxel, Mustapha Ishak Published in*" Effect of inhomogeneities on high precision measurements of cosmological distances "***Physical Review D**90, (2014) 123536. Paper available at http://arxiv.org/abs/1408.4390.

, M. A. Troxel, Mustapha Ishak, Austin Peel Published in*" The effects of structure anisotropy on lensing observables in an exact general relativistic setting for precision cosmology "***JCAP**1403:040, (2014). Paper available at http://arxiv.org/abs/1311.5936.

, Mustapha Ishak, Austin Peel, M.A. Troxel Published in*" Stringent Restriction from the Growth of Large-Scale Structure on Apparent Acceleration in Inhomogeneous Cosmological Models. "***Physical Review Letters**111, (2013) 251302. Paper available at http://arxiv.org/abs/1307.0723.

, Jason Dossett, Mustapha Ishak Published in*" Effects of Dark Energy Perturbations on Cosmological Tests of General Relativity "***Physical Review D**88, (2013) 103008. Paper available at http://arxiv.org/abs/1311.0726.

, M.A. Troxel, Mustapha Ishak Published in*" Effects of anisotropy on gravitational infall in galaxy clusters using an exact general relativistic model. "***JCAP**12 (2013) 048. Paper available at http://arxiv.org/abs/1311.5651.

, Austin Peel, Mustapha Ishak, M.A. Troxel Published in*" Large-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data. "***Physical Review D**86 (2012) 123508. Paper available at http://arxiv.org/abs/1212.2298.

, Mustapha Ishak, Austin Peel. Published in*" The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era. "***Physical Review D**85 (2012) 083502. Paper available at http://arxiv.org/abs/1104.2590.

, M. A. Troxel, Mustapha Ishak, Published in*" Self-Calibration Technique for 3-point Intrinsic Alignment Correlations in Weak Lensing Surveys. "***Monthly Notices of the Royal Astronomy Society**419 (2012) 1804. Paper available at http://arxiv.org/abs/1109.4896.

, 2. M. A. Troxel, Mustapha Ishak, Published in*" Self-calibrating the gravitational shear-intrinsic ellipticity-intrinsic ellipticity (GII) cross-correlation. "***Monthly Notices of the Royal Astronomy Society**427 (2012) 442. Paper available at http://arxiv.org/abs/1205.1547.

, Jason Dossett, Mustapha Ishak. Published in*" Spatial curvature and cosmological tests of general relativity. "***Physical Review D**86 (2012) 103008. Paper available at http://arxiv.org/abs/1205.2422.

, 2. M. A. Troxel, Mustapha Ishak, Published in*" Self-Calibration for 3-point Intrinsic Alignment Auto-Correlations in Weak Lensing Surveys. "***Monthly Notices of the Royal Astronomy Society**423 (2012) 1663. Paper available at http://arxiv.org/abs/1203.2138.

, 7. Jason Dossett, Mustapha Ishak, Jacob Moldenhauer. Published in*" Testing General Relativity at Cosmological Scales: Implementation and Parameter "***Physical Review D**84, 123001 (2011). Paper available at http://arxiv.org/abs/1109.4583.

, Jason Dossett, Jacob Moldenhauer, Mustapha Ishak. Published in*" Figures of merit and constraints from testing General Relativity using the latest cosmological data sets including refined COSMOS 3D weak lensing "***Physical Review D**84, 023012 (2011). Paper available at astro-ph:arXiv:1006.0014.

, Mustapha Ishak, Wolfgang Rindler, Jason Dossett. Invited Review Article Published in*" The Relevance of the Cosmological Constant for Lensing "***General Relativity and Gravitation**42: 2247-2268 (2010). Paper available at astro-ph:arXiv:1006.0014.

, Anthony Nwankwo, Mustapha Ishak, John Thompson. Published in*" Luminosity distance and redshift in the Szekeres inhomogeneous cosmological models "***JCAP**JCAP (2011). Paper available at astro-ph:arXiv:1006.0014.

, Jason Dossett, Mustapha Ishak, Jacob Moldenhauer, Yungui Gong, Anzhong Wang. Published in*" Constraints on growth index parameters from current and future observations "***JCAP**1004:022 (2010). Paper available at astro-ph:arXiv:1004.3086.

, Jacob Moldenhauer, Mustapha Ishak, John Thompson, Damien A. Easson. Published in*" Supernova, baryon acoustic oscillations, and CMB surface distance constraints on f(G) higher order gravity models "***Physical Review D**81, 063514 (2010). Paper available at astro-ph:arXiv:1004.2459.

Jacob Moldenhauer, Mustapha Ishak.. Published in*" A minimal set of invariants as a systematic approach to higher order gravity models II: Physical and Cosmological Constraints"***Journal of Cosmology and Astroparticle Physics**0912: 020 (2009). Paper available at astro-ph:arXiv:0912.5332.

, Yungui Gong, Mustapha Ishak, Anzhong Wang Published in*" Growth factor parametrization in curved space"***Physical Review D**80, 023002 (2009). Paper available at astro-ph:arXiv:0903.0001.

Mustapha Ishak, Jacob Moldenhauer. Published in*" A minimal set of invariants as a systematic approach to higher order gravity models"***Journal of Cosmology and Astroparticle Physics**0901: 024 (2009). Paper available at astro-ph:arXiv:0808.0951.

, Mustapha Ishak, Wolfgang Rindler, Jason Dossett,*" More on Lensing by a Cosmological Constant"***Monthly Notices of the Royal Astronomical Society Journal,**at press February 2010. astro-ph:arXiv:0810.4956.

Mustapha Ishak, James Richardson, Delilah Whittington, David Garred, Roberto Sussman. Published in*" Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?"***Physical Review D.**78, 123531, (2008). Paper available at astro-ph:0708.2943.

Mustapha Ishak. Published in*" Light Deflection, Lensing, and Time Delays from Gravitational Potentials and Fermat's Principle in the Presence of a Cosmological Constant"***Physical Review D.**78, 103006, (2008). Paper available at astro-ph:0708.2943.

Mustapha Ishak, Wolfgang Rindler, Jason Dossett, Jacob. Moldenhauer, Chris Allison.*" A new independent limit on the cosmological constant/dark energy from the relativistic bending of light by Galaxies and clusters of Galaxies"***Monthly Notices of the Royal Astronomical Society Journal,**Volume 388, Issue 3, p1279 (2008) astro-ph:arXiv:0710.4726.

James Richardson, Mustapha Ishak.*" Inverse approach to Einstein's equations for fluids with vanishing anisotropic stress tensor. "***Physical Review D.**77 (2008) 044005. Paper available at gr-qc:0707.135.

Wolfgang Rindler and Mustapha Ishak Physical Review D, 71, 023002 (2007) . Paper available at astro-ph:0709.2948 .*" The Contribution of the Cosmological Constant to the Relativistic Bending of light Revisited "*

Mustapha Ishak. Foundations of Physics, Volume 37, Number 10, (2007) 1470-1498 . Paper available at astro-ph/0504416.*" Remarks on the formulation of the cosmological constant/dark energy questions(2007) "*

(2007) Christopher M. Hirata, Rachel Mandelbaum, Mustapha Ishak, Uros Seljak, Robert Nichol, Kevin A. Pimblet, Nicholas P. Ross, David Wake.*" Intrinsic galaxy alignments from the 2SLAQ and SDSS surveys: luminosity and redshift scalings and implications for weak lensing surveys(2007) "***Monthly Notices of the Royal Astronomical Society**volume 381, 1197-1218 (2007). Paper available at astro-ph/0701671 .

Mustapha Ishak, Amol Upadhye, David N. Spergel (2005). Preprint available at astro-ph/0507184. strong>Physical Review D, 74, 043513 (2006).*"Probing Cosmic Acceleration Beyond the Equation of State: Distinguishing between Dark Energy and Modified Gravity Models"*

Or click here at NASA' Beyond Einstein web site.

Or related article in Astronomy Magazine.

Mustapha Ishak (2005). Monthly Notices of the Royal Astronomical Society, V363, issue 2, p469 (2005) . Paper available at astro-ph/0501594 .*"Probing decisive answers to dark energy questions from cosmic complementarity and lensing tomography"*

Amol Upadhye, Mustapha Ishak, Paul J. Steinhardt (2004). Physical Review D, 72, 063501 (2005) . Preprint available at astro-ph/0411803 .*"Dynamical dark energy: Current constraints and forecasts"*

Rachel Mandelbaum, Christopher M. Hirata, Mustapha Ishak, Uros Seljak, Jonathan Brinkmann (2005). Preprint available at astro-ph/0509026.*"Detection of large scale intrinsic ellipticity-density correlation from the Sloan Digital Sky Survey and implications for weak lens ing surveys"***Monthly Notices of the Royal Astronomical Society, 367 (2006) 611-626.**

Mustapha Ishak and Christopher M. Hirata (2004). Physical Review D, 71, 023002 (2005) . Paper available at astro-ph/0405042 .*"Spectroscopic source redshifts and parameter constraints from weak lensing and CMB"*

Mustapha Ishak, Christopher M. Hirata, Patrick McDonald, Uros Seljak (2003). Physical Review D, 69, 083914 (2004) . Paper available at astro-ph/0308446 .*"Weak Lensing and CMB: Parameter forecasts including a running spectral index"*

Mustapha Ishak (2003). Physical Review D, 69 , 124027 (2004) . Paper available at gr-qc/0405099 .**"On Perfect Fluid Models In Non-Comoving Null (Observational) Spherical Coordinates,**"

Mustapha Ishak and Kayll Lake (2003). Physical Review D, 68 , 104031 (2003) . Paper available at gr-qc/0304065 .**"An Inverse Approach to Einstein's Equations for non-conducting fluids"**

Roberto A. Sussman and Mustapha Ishak.**"Adiabatic Models of the Cosmological Radiative Era,"****General Relativity and Gravitation, Vol. 34, No. 10, (2002).**Paper available at gr-qc/0111010 .

Ishak Mustapha and Kayll Lake. Physical Review D, 65 , 044011 (2002) . Paper also available at gr-qc/0108058.**"Stability of Transparent Spherically Symmetric Thin Shells and Wormholes,"**

Mustapha Ishak and Kayll Lake. ,Classical and Quantum Gravity, 19 , 505-514 (2002) . Paper also available at gr-qc/0111008 . GRDB Version 1.0 was released on July 2001, and is available at http://grdb.org.**"Interactive Geometric Database, Including Exact Solutions of Einstein's Field Equations,"**

Nicholas Neary, Mustapha Ishak and Kayll Lake. Physical Review D, 64, 028001 (2001) . Paper also available at gr-qc/0104002.**"The Tolman VII solution, trapped null orbits and w-modes,"**

Mustapha Ishak, Luke Chamandy, Nicholas Neary and Kayll Lake. Physical Review D, 64, 024005 (2001) .Paper also available at gr-qc/0007073.*"Exact solutions with w-modes,"*

*The Dark Energy Science Collaboration (DESC) of the Large Synoptic Survey Telescope (LSST)*.

*The Sloan Digital Sky Survey (SDSS)*.

*Canada-France-Hawaii Telescope Legacy Survey (CFHTLS)*.

*The Terrestrial Planet Finder (TPF-C)*. Auxiliary Science: Dark Energy and Cosmology (using very high redshift supernovae)

*GRTensorJ software*. A graphical user interface to GRTensorII, the foremost computer syStem for doing tensor and algebraic calculations in General Relativity, String Theory and Cosmology.

*http://grdb.org software*. (GRDB): An online interactive geometric database that includes exact solutions of Einstein's Field Equations. GRDB integrates the virtual calculator GRTensorJ to do extremely complicated tensor, tetrad, basis calculations online. We used Java, C, Maple and other web-based technologies.

ISiTGR (Integrated Software in Testing General Relativity.)

Visits since October 24th, 2016