Abstract
We will present main results of our recent investigations on the existence of the Schwarzschild-Tangherlini black holes in a five-dimensional (nonlinear) massive gravity as well as in its dynamical extension, a five-dimensional massive bi-gravity. In particular, we will show how to use the well-known Cayley-Hamilton theorem to construct five-and higher dimensional massive graviton terms. Then, we will present the proof of the existence of the Schwarzschild-Tangherlini black holes in the five-dimensional massive (bi-)gravity.
Highlights
IntroductionIn 1939, Fierz and Pauli proposed a modification of the Einstein’s general relativity (GR), in which the graviton is assumed to have a tiny but not vanishing mass mg [1]
In 1939, Fierz and Pauli proposed a modification of the Einstein’s general relativity (GR), in which the graviton is assumed to have a tiny but not vanishing mass mg [1]. This massive gravity theory was shown by van Dam-Veltman and Zakharov in 1970 that it will not reduce to the GR in the limit mg → 0 [2, 3]
Vainshtein proposed that nonlinear massive graviton terms might solve this discontinuity once they are introduced to the FP theory [4]
Summary
In 1939, Fierz and Pauli proposed a modification of the Einstein’s general relativity (GR), in which the graviton is assumed to have a tiny but not vanishing mass mg [1] This massive gravity theory was shown by van Dam-Veltman and Zakharov (vDVZ) in 1970 that it will not reduce to the GR in the limit mg → 0 [2, 3]. Some papers have studied higher dimensional black holes in the framework of the dRGT theory with only the first three massive graviton terms L2, L3, and L4 [15].
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