[Paper Review] Massless black holes and charged wormholes in string theory

Prieslei Goulart|arXiv (Cornell University)|Nov 10, 2016

Black Holes and Theoretical Physics1 references5 citations

TL;DR

This paper constructs massless pointlike black holes and static, traversable charged wormholes in string theory using the Einstein-Maxwell-dilaton (EMD) framework. By fine-tuning integration constants in the dyonic black hole solution, it derives a massless non-extremal black hole with real physical observables and a charged wormhole that satisfies the null energy condition without exotic matter, offering a new class of solutions distinct from paired massless black holes.

ABSTRACT

We discuss the zero mass pointlike solutions and charged Einstein-Rosen bridges (wormholes) that arise from the dyonic black hole solution of the Einstein-Maxwell-dilaton theory. These massless black holes exist individually in spacetime, different from the known massless solutions, which come in pairs with opposite signs for their masses. In order to construct a massless object, we choose the integration constants of the solution to have specific values. The massless solutions present some problems: in one case the dilaton field is complex (or the gauge field has negative kinetic energy), and in the other case the solution has negative entropy and temperature or it is naked singularity in the extremal limit. For the first case, the observables computed are real quantities. This massless solution also allow the bridge construction, and we obtain an analytical and static charged wormhole solution, which satisfies the null energy condition.

Motivation & Objective

• To explore the existence of individual massless black holes in string theory, distinct from paired solutions with opposite masses.
• To resolve the issue of negative energy or complex fields in massless solutions by selecting specific integration constants.
• To construct a static, traversable charged wormhole from a massless black hole solution that satisfies the null energy condition.
• To analyze whether such solutions are physically acceptable despite complex dilaton fields or negative kinetic energy in the gauge sector.
• To investigate the implications for traversability and stability of massless black holes and wormholes in EMD theory.

Proposed method

• Derives the dyonic black hole solution in Einstein-Maxwell-dilaton (EMD) theory with specific integration constants to achieve zero ADM mass.
• Applies a coordinate transformation to reveal a bridge structure, identifying the solution as a charged Einstein-Rosen wormhole.
• Computes the energy-momentum tensor components (ρ, τ, p) to evaluate the null energy condition (NEC) in the static observer frame.
• Evaluates the NEC condition ρ(r) - τ(r) ≥ 0 and shows it is satisfied for the wormhole solution, especially at the critical point Σ = 0.
• Analyzes physical observables—mass, charge, entropy, temperature, dilaton charge—confirming they are real despite complex dilaton or negative kinetic energy in some cases.
• Uses the metric and field equations in Gaussian normal coordinates to verify the static, spherically symmetric nature of the wormhole solution.

Experimental results

Research questions

• RQ1 Can massless black holes exist as individual solutions rather than in pairs with opposite masses in EMD theory?
• RQ2 Does a massless non-extremal black hole solution with real physical observables exist despite complex dilaton or negative gauge field kinetic energy?
• RQ3 Can a static, charged wormhole be constructed from such a massless black hole that satisfies the null energy condition without exotic matter?
• RQ4 What is the role of the dilaton field and integration constants in achieving zero ADM mass and physical consistency?
• RQ5 Is the resulting wormhole traversable, and does it avoid singularities or naked singularities in the extremal limit?

Key findings

• The paper constructs a massless non-extremal black hole solution with zero ADM mass by setting specific values for integration constants, distinct from paired solutions.
• Physical observables—mass, electric and magnetic charges, entropy, temperature, and dilaton charge—are all real, despite the dilaton field being complex at infinity or the gauge field having negative kinetic energy.
• A static, charged wormhole solution is derived from the massless black hole, satisfying the null energy condition (NEC) without requiring exotic matter.
• The NEC is verified via the expression ρ(r) - τ(r) = (d₀ - d₁)²(r² - r₀²) / [2(d₀ + r)³(d₁ + r)³], which is non-negative for the constructed solution.
• At the critical point Σ = 0, the NEC bound is saturated, indicating a special configuration where energy conditions are marginally satisfied.
• The solution avoids naked singularities in the extremal limit and presents a new class of massless pointlike objects not previously known in EMD theory.