<p>We present an analysis of phantom energy dominated conformal cyclic baby universes evolving inside black holes. For stable black holes, the analysis yields an infinite sequence of conformal cycles. This sequence terminates at a critical number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$n_{\text {crit}} \approx \epsilon ^{-1}\ln (2M_0/\ell _{\text {Pl}})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>n</mi> <mtext>crit</mtext> </msub> <mo>≈</mo> <msup> <mi>ϵ</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>ln</mo> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <msub> <mi>M</mi> <mn>0</mn> </msub> <mo stretchy="false">/</mo> <msub> <mi>ℓ</mi> <mtext>Pl</mtext> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. At this point, the interior approaches a Planck-scale remnant in finite proper time. For evaporating BHs, the discussed solutions indicate that a phantom-dominated interior branch can outgrow the shrinking horizon if <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$b_0 > 2M_0(\tau _s - v_0)^{-\mu /3}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>></mo> <mn>2</mn> <msub> <mi>M</mi> <mn>0</mn> </msub> <msup> <mrow> <mo stretchy="false">(</mo> <msub> <mi>τ</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>v</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mo>-</mo> <mi>μ</mi> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. These timescales are shorter than Hawking evaporation. The model exhibits a possible semiclassical avoidance of the Schwarzschild singularity via effective LQG dynamics. A phantom-dominated branch extends the interior evolution beyond the bounce. The conformal mapping suggests, at a heuristic level, a possible channel for information leakage. We discuss possible observational signatures, such as gravitational-wave echoes and CMB circular anomalies. We also discuss a complex-time formulation that captures the accumulation of cycles.</p>

Conformal Cyclic Baby Universes in Evaporating Black Holes

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发表日期：

2025年11月3日

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Natarajan Shriethar

摘要

We present an analysis of phantom energy dominated conformal cyclic baby universes evolving inside black holes. For stable black holes, the analysis yields an infinite sequence of conformal cycles. This sequence terminates at a critical number $n_{\text {crit}} \approx \epsilon ^{-1}\ln (2M_0/\ell _{\text {Pl}})$ $n_{crit} \approx ϵ^{- 1} ln (2 M_{0} / ℓ_{Pl})$ . At this point, the interior approaches a Planck-scale remnant in finite proper time. For evaporating BHs, the discussed solutions indicate that a phantom-dominated interior branch can outgrow the shrinking horizon if $b_0 > 2M_0(\tau _s - v_0)^{-\mu /3}$ $b_{0} > 2 M_{0} {(τ_{s} - v_{0})}^{- μ / 3}$ . These timescales are shorter than Hawking evaporation. The model exhibits a possible semiclassical avoidance of the Schwarzschild singularity via effective LQG dynamics. A phantom-dominated branch extends the interior evolution beyond the bounce. The conformal mapping suggests, at a heuristic level, a possible channel for information leakage. We discuss possible observational signatures, such as gravitational-wave echoes and CMB circular anomalies. We also discuss a complex-time formulation that captures the accumulation of cycles.