[Paper Review] Global Causal Structure of a Transient Black Object

Tehani K. Finch, James Lindesay|arXiv (Cornell University)|Oct 31, 2011

Quantum Electrodynamics and Casimir Effect11 references3 citations

TL;DR

This paper constructs a singularity-free, spherically symmetric transient black object with a timelike center and no event horizon, using a dynamic metric parameterized by 'river time' to model accretion and evaporation. The geometry exhibits a trapped region where all causal trajectories move inward, yet information can be fully recovered after evaporation, with entanglement preserved across the transient phase.

ABSTRACT

A singularity-free and spherically symmetric transient black object whose center remains always timelike, yet directly manifests a trapped region, has been constructed and numerically implemented. The exterior geometry is shown to be similar to that of a long-lived transient black hole, with a few subtle differences. The large-scale global structure of the geometry is examined through the construction of a conformal diagram, which exhibits no event horizon and bears resemblance to that of a Minkowski spacetime. Since there is no singularity within the geometry, the evolution of the exchange of information between timelike observers, including those that fall through the trapped region, can be directly explored. The dynamics of generic "standard" communications, as well as entangled communications, is exhibited through both t-versus-r and conformal spacetime diagrams.

Motivation & Objective

• To develop a dynamic, singularity-free black object model that avoids event horizons while preserving trapped regions for temporary information storage.
• To construct a spacetime geometry satisfying all energy conditions during accretion and evaporation, ensuring physical consistency.
• To explore causal structure and information dynamics in a horizon-free, transient black object using conformal diagrams and spacetime trajectories.
• To examine the behavior of classical and quantum communications—especially entangled photons—through the transient geometry.
• To demonstrate that information and entanglement are not permanently lost, even when temporarily trapped in the region

Proposed method

• The metric is derived from a non-orthogonal coordinate system inspired by river models, with time dependence parameterized by 'river time' instead of Schwarzschild time.
• The radial mass scale $ R_M(ct,r) = 2G_N M(ct,r)/c^2 $ is used to define the geometry, ensuring analyticity and absence of singularities at $ r=0 $.
• Geometrically stationary observers are defined by $ u^{ct}_{ ext{obs}} = 1 $, enabling a global time foliation compatible with asymptotic observers.
• Lightlike and timelike geodesics are computed to analyze causal structure, particularly near the trapped region.
• Conformal diagrams are constructed to visualize the global causal structure, showing no event horizon and resemblance to Minkowski spacetime.
• Outgoing photon emissions from infalling observers are modeled to study redshift and emission rate dynamics, including entangled photon pairs

Experimental results

Research questions

• RQ1 Can a transient black object be constructed without a singularity or event horizon while still exhibiting a trapped region?
• RQ2 How does the causal structure of such a geometry differ from that of a classical black hole, particularly in terms of global foliation and conformal structure?
• RQ3 What happens to information and entanglement when particles or photons pass through the trapped region of a transient black object?
• RQ4 How do energy shifts and time delays affect the observation of outgoing signals from an infalling emitter in this dynamic geometry?
• RQ5 Can energy conditions be satisfied throughout the accretion and evaporation phases of such a transient object?

Key findings

• The geometry is globally analytic and free of singularities, with the center $ r=0 $ remaining timelike throughout the spacetime evolution.
• No event horizon forms, and the conformal diagram shows a structure similar to Minkowski spacetime, with only a minimal modification due to the transient trapped region.
• Outgoing photons from an infalling emitter experience significant redshift as the emitter approaches the trapped region, with the energy ratio $ ho o 0 $ as the emitter nears the center.
• Information temporarily trapped in the region is fully recoverable after the object evaporates, with no permanent loss or violation of quantum information principles.
• Entangled photon pairs, with one photon crossing the trapped region, show temporal and energy shifts: Alice measures $ ho o 0.01 $, Bob measures $ ho o 8 imes 10^{-8} $, indicating redshifted and delayed detection.
• The dynamics of communication and entanglement are consistent with standard quantum and relativistic laws, with no evidence of information loss or non-locality violations