Leading higher-derivative corrections to Kerr geometry
- PDF / 2,384,649 Bytes
- 50 Pages / 595.276 x 841.89 pts (A4) Page_size
- 70 Downloads / 211 Views
Springer
Received: January 30, Revised: April 5, Accepted: May 5, Published: May 28,
2019 2019 2019 2019
Pablo A. Cano and Alejandro Ruip´ erez Instituto de F´ısica Te´ orica UAM/CSIC, C/Nicol´ as Cabrera, 13-15, C.U. Cantoblanco, 28049 Madrid, Spain
E-mail: [email protected], [email protected] Abstract: We compute the most general leading-order correction to Kerr solution when the Einstein-Hilbert action is supplemented with higher-derivative terms, including the possibility of dynamical couplings controlled by scalars. The model we present depends on five parameters and it contains, as particular cases, Einstein-dilaton-Gauss-Bonnet gravity, dynamical Chern-Simons gravity and the effective action coming from Heterotic Superstring theory. By solving the corrected field equations, we find the modified Kerr metric that describes rotating black holes in these theories. We express the solution as a series in the spin parameter χ, and we show that including enough terms in the expansion we are able to describe black holes with large spin. For the computations in the text we use an expansion up to order χ14 , which is accurate for χ < 0.7, but we provide as well a Mathematica notebook that computes the solution at any given order. We study several properties of the corrected black holes, such as geometry of the horizon, ergosphere, light rings and scalar hair. Some of the corrections violate parity, and we highlight in those cases plots of horizons and ergospheres without Z2 symmetry. Keywords: Black Holes, Classical Theories of Gravity, Black Holes in String Theory ArXiv ePrint: 1901.01315
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)189
JHEP05(2019)189
Leading higher-derivative corrections to Kerr geometry
Contents 1 Introduction
1
2 Leading order effective theory 2.1 Equations of motion
4 7 8 11
4 Properties of the corrected black hole 4.1 Horizon 4.2 Ergosphere 4.3 Photon rings 4.4 Scalar hair
13 13 19 22 28
5 Conclusions
30
A Higher-derivative gravity with dynamical couplings
32
B Compactification and truncation of the effective action of the Heterotic String 35 C The solution
37
D Convergence of the χ-expansion
40
E Some formulas
42
1
Introduction
General Relativity (GR) describes the gravitational interaction as the effect of spacetime curvature. Einstein’s field equations, that rule the dynamics of the gravitational field, can be derived from the Einstein-Hilbert (EH) action Z p 1 S= d4 x |g|R , (1.1) 16πG which is essentially the simplest non-trivial covariant action one can write for the metric tensor. This beautiful theory has passed a large number of experimental tests — including the recent detection of gravitational waves coming from black hole and neutron star binaries [1–6]— and it is broadly accepted as the correct description of the gravitational interaction.
–1–
JHEP05(2019)189
3 The corrected Kerr metric 3.1 Solving the equations
1
See e.g. [10–13] for other possible extensions of GR.
–2–
JHEP05(2019)189
Howeve
Data Loading...
