[Paper Review] Black Holes in brane worlds

P. Surànyi, L. C. R. Wijewardhana|ArXiv.org|Jul 9, 2002

Black Holes and Theoretical Physics1 references3 citations

TL;DR

This paper investigates black hole stability in Randall-Sundrum brane world models (RS1 and RS2), using a perturbative expansion to analyze 4D and 5D black holes localized on the TeV brane. It finds two distinct instability regimes: 4D black holes decay into 5D black holes at a critical mass of ~10^32 TeV due to entropy gain, while 5D black holes on the brane become unstable above ~10^3 TeV, indicating a gap in stable black hole masses in RS1.

ABSTRACT

In a Randall-Sundrum theory (RS1) 3+1 dimensional black holes and higher dimensional black holes are not the natural continuations of each other. 3+1 dimensional black holes decay into a large number of 4+1 dimensional black holes at a critical mass, $M_{ m crit}\sim 10^{32}$ TeV. Those black holes themselves may become unstable above another, albeit much smaller critical mass, $M_0\sim 10^3$TeV.

Motivation & Objective

• To understand the stability and decay mechanisms of black holes in warped extra dimension models like RS1 and RS2.
• To determine whether 4D black holes on the TeV brane can transition into 5D black holes via quantum fluctuations.
• To identify critical masses at which entropy-driven instabilities occur, using entropy arguments and effective field theory.
• To explore the implications of these instabilities for black hole production and accretion in early universe cosmology.
• To compare the behavior of black holes in RS1 (two-brane) and RS2 (single-brane) models, particularly regarding horizon size and stability thresholds.

Proposed method

• Uses a perturbative expansion technique to construct black hole solutions in the RS1 model, treating the 5D metric as a deformation of flat space.
• Applies a conformal coordinate transformation to map the warped geometry into a form where the TeV brane is at w=0 and the Planck brane at w = z_c - λ.
• Derives the effective 5D action with rescaled Planck mass M_5 = M_5 * (λ / z_c), setting M_5 ~ 1 TeV for phenomenological consistency.
• Compares the entropy of 4D and 5D Schwarzschild black holes of equal mass to identify a critical mass M_crit where 5D black holes become entropically favored.
• Applies similar entropy-based arguments to RS2, where the AdS curvature length λ sets a scale for the transition from 4D to 5D behavior.
• Uses the Myers-Perry solution as a starting point for 5D black holes and analyzes their stability near the AdS scale λ.

Experimental results

Research questions

• RQ1 At what critical mass does a 4D black hole on the TeV brane in RS1 become unstable and decay into multiple 5D black holes due to entropy gain?
• RQ2 Why is the instability threshold in RS1 (~10^32 TeV) so much higher than in the ADD model, and how does the warped geometry alter the decay dynamics?
• RQ3 What determines the upper mass limit (~10^3 TeV) for stable 5D black holes in the RS1 model, and why is there a gap in stable black hole masses between 10^3 TeV and 10^32 TeV?
• RQ4 How does the accretion of plasma affect primordial black holes in RS1 when the ambient temperature is ~1 TeV?
• RQ5 Can the AdS-CFT correspondence provide insight into the stability and growth of TeV-scale black holes in RS2 models?

Key findings

• In RS1, 4D black holes on the TeV brane decay into a large number (~10^29) of 5D black holes at a critical mass M_crit ~ 10^32 TeV, where the entropy of the 5D configuration exceeds that of the 4D one.
• The 5D black holes formed at M_crit have a horizon radius R ~ z_c, comparable to the size of the 4D black hole, and a Hawking temperature of order 1 TeV.
• Above a second critical mass M_0 ~ 10^3 TeV, 5D black holes on the brane become unstable and decay into two black holes of mass M_0 ~ 10^3 TeV, indicating a second instability threshold.
• The instability in RS1 differs fundamentally from the Gregory-Laflamme instability in flat space, as 5D black holes in RS1 are most stable at R ~ z_c, not at larger sizes.
• In RS2, 4D black holes become unstable at M_crit ~ λ M_4^2 ~ 10^32 M_4, corresponding to ~10^32 TeV, where they transition into 5D black holes due to entropy gain.
• For M_4 ~ 1 TeV, the critical mass M_crit ~ 10^32 TeV, and the number of 5D black holes produced is estimated as N ~ M_crit / M_0 ~ 10^29, consistent with entropy maximization.