Yüksek sayıda boyutlara sahip kütle çekim teorisi

General Relativity is succesful in understanding the phenomena such as light bending by the Sun and the perihelion precession of Mercury that could not be understood in Newton's gravity. Within solar system scales, General Relativity is a very powerful theory but for very small or very large distances, the theory has non-renormalization issues and lack of explanation of the accelerated expansion of the universe and the galaxy rotation curves which give a hint at the need for modifications. In this thesis, Born-Infeld type modifications of General Relativity are considered. In 1998 Deser and Gibbons proposed Born-Infeld gravity theory that has some common features with the Eddington's gravitational action and the Born-Infeld electrodynamics. The Born-Infeld gravity theory, like the other two, has a determinantal action but the free variable of the theory is the metric not the connection as in the Eddington's gravity theory. In this thesis we have calculated the Wald entropy of the Born-Infeld gravity theories and showed that this dynamical entropy reduces to the geometric Bekenstein- Hawking entropy with the appropriate choice of effective gravitational constant. We also discuss black hole entropy in generic dimensions for the Born-Infeld theories.