Kasner eons in Lovelock black holes

In the vicinity of spacelike singularities, general relativity predicts that the metric behaves, at each point, as a Kasner space which undergoes a series of “Kasner epochs” and “eras” characterized by certain transition rules. The period during which this process takes place defines a “Kasner eon,” which comes to an end when higher-curvature or quantum effects become relevant. When higher-curvature densities are included in the action, spacetime can undergo transitions into additional Kasner eons. During each eon, the metric behaves locally as a Kasner solution to the higher-curvature density controlling the dynamics. In this paper we identify the presence of Kasner eons in the interior of static and spherically symmetric Lovelock gravity black holes. We determine the conditions under which eons occur and study the Kasner metrics which characterize them, as well as the transitions between them. We show that the null energy condition implies a monotonicity property for the effective Kasner exponent at the end of the Einsteinian eon. We also characterize the Kasner solutions of more general higher-curvature theories of gravity. In particular, we observe that the Einstein gravity condition that the sum of the Kasner exponents adds up to 1,

\sum_{i = 1}^{D - 1} p_{i} = 1

, admits a universal generalization in the form of a family of Kasner metrics satisfying

\sum_{i = 1}^{D - 1} p_{i} = 2 n - 1

which exists for any order-

n

higher-curvature density and in general dimensions.

Note:

27 pages, 5 figures

References(57)

Figures(18)

[1]

Cambridge Monographs on Mathematical Physics (, Cambridge, England, ), p.

S.W. Hawking
,
G.F.R. Ellis

[2]

Oscillatory approach to a singular point in the relativistic cosmology

- Adv.Phys. 19 (1970) 525-573
•
DOI:
- 10.1080/00018737000101171

[3]

One loop divergencies in the theory of gravitation

G. 't Hooft
,
M.J.G. Veltman

- Ann. Inst. Henri Poincare Phys. Theor. A 20 (1974) 69

[4]

The Ultraviolet Behavior of Einstein Gravity

Marc H. Goroff
(
- Caltech
)
,
Augusto Sagnotti
(
- UC, Berkeley and
- LBL, Berkeley
)

- Nucl.Phys.B 266 (1986) 709-736
•
DOI:
- 10.1016/0550-3213(86)90193-8

[5]

The Quartic Effective Action for the Heterotic String

David J. Gross
(
- UC, Santa Barbara and
- Princeton U.
)
,
John H. Sloan
(
- UC, Santa Barbara and
- Princeton U.
)

- Nucl.Phys.B 291 (1987) 41-89
•
DOI:
- 10.1016/0550-3213(87)90465-2

[6]

$\sigma$ Model Superstring Corrections to the Einstein-hilbert Action

Marcus T. Grisaru
(
- Brandeis U.
)
,
D. Zanon
(
- Harvard U.
)

- Phys.Lett.B 177 (1986) 347-351
•
DOI:
- 10.1016/0370-2693(86)90765-3

[7]

Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation

A.D. Sakharov
(
- Unlisted
)

- Gen.Rel.Grav. 32 (2000) 2, 365-367,
- Dokl.Akad.Nauk SSSR 177 (1967) 1, 70-71
•
DOI:
- 10.1023/A:1001947813563

[8]

Sakharov's induced gravity: A Modern perspective

Matt Visser
(
- Washington U., St. Louis
)

- Mod.Phys.Lett.A 17 (2002) 977-992
•
e-Print:
- gr-qc/0204062
•
DOI:
- 10.1142/S0217732302006886

[9]

An effective formalism for testing extensions to General Relativity with gravitational waves

Solomon Endlich
(
- Stanford U., ITP
)
,
Victor Gorbenko
(
- Stanford U., ITP
)
,
Junwu Huang
(
- Stanford U., ITP
)
,
Leonardo Senatore
(
- Stanford U., ITP
)

- JHEP 09 (2017) 122
•
e-Print:
- 1704.01590
•
DOI:
- 10.1007/JHEP09(2017)122

[10]

Holographic flows from CFT to the Kasner universe

- JHEP 08 (2020) 003
•
e-Print:
- 2004.01192
•
DOI:
- 10.1007/JHEP08(2020)003

[11]

Gravitational duals to the grand canonical ensemble abhor Cauchy horizons

- JHEP 10 (2020) 102
•
e-Print:
- 2006.10056
•
DOI:
- 10.1007/JHEP10(2020)102

[12]

No Inner-Horizon Theorem for Black Holes with Charged Scalar Hairs

Rong-Gen Cai
(
- Beijing, Inst. Theor. Phys.
)
,
Li Li
(
- Beijing, Inst. Theor. Phys.
)
,
Run-Qiu Yang
(
- Tianjin U.
)

- JHEP 03 (2021) 263
•
e-Print:
- 2009.05520
•
DOI:
- 10.1007/JHEP03(2021)263

[13]

What’s inside a hairy black hole in massive gravity?

Seyed Ali Hosseini Mansoori
(
- Shahrood U.
)
,
Li Li
(
- Beijing, Inst. Theor. Phys. and
- HIAS, UCAS, Hangzhou
)
,
Morteza Rafiee
(
- Shahrood U.
)
,
Matteo Baggioli
(
- Shanghai Jiaotong U.
)

- JHEP 10 (2021) 098,
- Journal of High Energy Physics volume 2021, Article number: 98 (2021)
•
e-Print:
- 2108.01471
•
DOI:
- 10.1007/JHEP10(2021)098