arXiv subjects

Justin C. Feng

Publications and source records attributed to Justin C. Feng.

At least 19 recordsLinked to original sources

arXiv2026

Redshifted civilizations, galactic empires, and the Fermi paradox

Given the vast distances between stars in the Milky Way and the long timescales required for interstellar travel, we consider how a civilization might overcome the constraints arising from finite lifespans and the speed of light without invoking exotic or novel physics. We consider several scenarios in which a civilization can migrate to a time-dilated frame within the scope of classical general relativity and without incurring a biologically intolerable level of acceleration. Remarkably, the power requirements are lower than one might expect; biologically tolerable orbits near the photon radius of Sgr A* can be maintained by a civilization well below the Type II threshold, and a single Type II civilization can establish a galaxy-spanning civilization with a time dilation factor of $10^4$, enabling trips spanning the diameter of the Milky Way within a human lifetime in the civilizational reference frame. We also find that isotropic, monochromatic signals from orbits near the photon radius of a black hole exhibit a downward frequency drift. The vulnerability of ultrarelativistic vessels to destruction, combined with the relatively short timescales on which adversarial civilizations can arise, provides a strong motivating element for the ``dark forest'' hypothesis.

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arXiv2026

The emergent Big Bang scenario

This paper proposes a new avenue for understanding the cosmological singularity. The standard cosmological model contains a generic initial singularity usually referred to as the {\em big bang}. Herein, we present a novel idea to extend the description of our Universe beyond this limit. The proposal relies on rewriting physics in a purely Riemannian, {\em i.e.} locally Euclidean, four-dimensional space and the emergence of Lorentzian patches owing to the interaction of all matter fields to a clock field that is responsible for a signature change. If our Universe is contained within one of these patches, the initial singularity is replaced by a smooth boundary on which the signature of the physical metric flips. In this paper, we first define the model and draw the necessary conditions on its arbitrary functions for solutions to exist. Next, we prove the existence of solutions that lead to an emergent universe with a primordial (almost) de Sitter phase. To finish, we discuss the consequences of this construction for the universe on scales much larger than our observable Universe: a large ``Euclidean sea'' in which Lorentzian islands locally emerge and host an expanding universe potentially similar to ours. While speculative, this scenario has specific features that can be tested, and the present paper sets the basis for further phenomenological investigations.

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arXiv2025

Aiming for Proxima Centauri b: Gravitational effects on relativistic spacecraft trajectories

How important are gravitational and relativistic effects for interstellar travel? We consider this question in the context of proposed laser-propelled spacecraft missions to neighboring stellar destinations. Our analysis applies to any spacecraft traveling at relativistic speeds. As a concrete example, we focus on a mission to Proxima Centauri b -- a terrestrial-sized planet in the habitable zone around our nearest stellar neighbor, Proxima Centauri. We employ a Julia reimplementation of the PoMiN code, an N-body code modeling relativistic gravitational dynamics in the first post-Minkowskian (PM) approximation to general relativity (valid to linear order in Newton's constant $G$). We compute the gravitational influence of seven different celestial bodies and find that the Sun has the greatest influence on the trajectory of the interstellar spacecraft. We also study the differences between Newtonian and PM gravity, and find that if mission planners wish to hit Proxima Centauri b with an accuracy of better than about 690,000 kilometers, relativistic effects must be taken into account. To solve for the precise initial data needed to hit an intended target, we develop numerical fine-tuning methods and demonstrate that these methods can (within a given model) be precise to about a femtometer over a travel distance of $\sim4.25$ light years. However, we find that for the spacecraft trajectories we consider, higher order general relativistic effects (beyond the first PM approximation) from the Sun can displace the final position of the spacecraft by tens of kilometers. We also consider the variation in the initial direction of the spacecraft velocity and find that, even with relativistic effects properly taken into account, the miss distances can be dominated by the variation in the initial velocity that could arise from errors during the launch and boost phase of the spacecraft mission.

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arXiv2025

Emergent Lorentzian dispersion relations from a Euclidean scalar-tensor theory

Can one be fooled into thinking that space and time are fundamentally described by a Lorentzian manifold? In this article, we describe a scenario in which a theory constructed on a (Euclidean signature) Riemannian manifold can lead to degrees of freedom with Lorentzian dispersion relations, due to a nontrivial configuration of a scalar field. In particular, we perform a perturbative analysis of a renormalizable shift-symmetric scalar-tensor theory and find that it can, in principle, admit a massless tensor degree of freedom with a Lorentzian dispersion relation. While the remaining degrees of freedom in the gravity sector will, in general, satisfy Euclidean dispersion relations, we argue that they can be brought under control by elliptic equations with an appropriate choice of boundary conditions.

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arXiv2025

Dust stars in the minimal exponential measure model

We report the existence of horizonless compact object solutions supported by dust in the Minimal Exponential Measure (MEMe) model, a theory which modifies the couplings between gravity and matter without introducing dynamical degrees of freedom. For a perfect fluid source, the field equations for the MEMe model can be rewritten as the Einstein field equations sourced by a perfect fluid with a transformed equation of state, which can endow a sufficiently dense cloud of dust with an effective pressure. The resulting dust-supported horizonless compact objects can have masses below $\sim 10^{-11}~M_\odot$, making them suitable as MACHOs comprising a significant mass fraction for dark matter. A necessary condition for the existence of these compact object solutions is that the single free parameter in the MEMe model is positive-valued. Additionally, we find that this positive sign for the parameter can provide a mechanism for suppressing the formation of (primordial) black holes from the gravitational collapse of matter below a certain mass scale.

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arXiv2025

An asymptotic systems approach for the good-bad-ugly model with application to general relativity

We employ an adapted version of Hörmander's asymptotic systems method to show heuristically that the standard good-bad-ugly model admits formal polyhomogeneous asymptotic solutions near null infinity. In a related earlier approach, our heuristics were unable to capture potential leading order logarithmic terms appearing in the asymptotic solution of the good equation (the standard wave equation). Presently, we work with an improved method which overcomes this shortcoming, allowing the faithful treatment of a larger class of initial data in which such logarithmic terms are manifest. We then generalize this method to encompass models that include stratified null forms as sources and whose wave operators are built from an asymptotically flat metric. We then apply this result to the Einstein field equations in generalized harmonic gauge and compute the leading decay in~$R^{-1}$ of the Weyl scalars, where~$R$ is a suitably defined radial coordinate. We detect an obstruction to peeling, a decay statement on the Weyl scalars~$Ψ_n$ that is ensured by smoothness of null infinity. The leading order obstruction appears in~$Ψ_2$ and, in agreement with the literature, can only be suppressed by a careful choice of initial

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arXiv2025

Cosmological constant as an integration constant

The discrepancy between the observed value of the cosmological constant (CC) and its expected value from quantum field theoretical considerations motivates the search for a theory in which the CC is decoupled from the vacuum energy. In this article, we consider the viability of theories in which the Einstein equations are recovered (without additional constraints) and in which the CC is regarded as an integration constant. These theories include trace-free Einstein gravity, theories constructed from the Codazzi equation (which includes Cotton gravity and a gauge-gravity inspired theory), and conformal Killing gravity. We remark on a recent debate regarding Cotton gravity and find that while the Codazzi equation of that theory is indeed underdetermined, the solutions of the Codazzi equation trivialize to $λg_{ab}$ on generic backgrounds, and that in principle, one can close the system with the divergence-free condition and an appropriate choice of initial data. We also propose a full variational principle (full in the sense that variations in all variables are considered) for each of the aforementioned theories that can incorporate the matter sector; in this manner, we can obtain the trace-free Einstein equations without a unimodular constraint. The resulting actions require additional (auxiliary) fields and are therefore only expected to be effective, but they may provide a useful starting point in bottom up approaches to constructing more fundamental theories.

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arXiv2024

Probing the quantum nature of black holes with ultra-light boson environments

Quantum black holes (BHs), thought of as an excited multilevel system, can be effectively modelled by replacing an event horizon with a partially reflective membrane. This emergent feature affects their interaction with hosting environments, with the most pronounced effects happening for particles with mass~$m_{\rm p}\lesssim (10 M_{\odot}/M)\,10^{-11}\mathrm{\,eV}$, where~$M$ is the BH mass. We show that ultra-light bosons -- a viable dark matter candidate -- can be used to probe the quantum nature of BHs. We derive analytical expressions for the accretion rate and dynamical friction acting on exotic compact objects moving through an ultra-light scalar field, finding that while the accretion rate is sensitive to the quantum BH's reflectivity, the dynamical friction is the same as for classical BHs. We then use these expressions to estimate the orbital dephasing in the inspiralling of different binaries in the Laser Interferometer Space Antenna (LISA) band. Our results indicate that LISA may be able to discriminate quantum from classical BHs through their different accretion rates.

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arXiv2024

Singularity at the demise of a black hole

We consider a class of quasiregular singularities characterized by points possessing two future-directed light cones and two past-directed light cones. Such singularities appear in the $1+1$ trousers spacetime and the Deutsch-Politzer spacetime. We argue that these singularities are relevant for describing the end point of an evaporating black hole, and show that a class of emergent Lorentz signature theories can provide a microscopic description for these singularities.

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arXiv2024

Gravity limits the kinetic energy of a massive elementary particle

In this note, I argue that tidal effects generically limit the kinetic energy of a single massive elementary particle in the vicinity of a compact object. As the kinetic energy is increased, the differences in the tidal potential over a Compton wavelength will at some point exceed the rest mass of the particle. Above the threshold, one expects tidal effects to disrupt single-particle states, and in turn, one might expect an incident particle scattering off a compact object with an energy significantly exceeding the threshold to result in a shower of lower energy particles. A calculation reveals that the threshold for neutrinos scattering off a $10 M_\odot$ black hole within three Schwarzschild radii is roughly $1~\text{GeV}$.

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arXiv2023

Smooth metrics can hide thin shells

In this note, I consider a class of metric tensors with smooth components that naively appear to describe dynamical wormholes with vanishing spacetime curvature. I point out that the smoothness of the metric tensor components is deceptive, and that in general relativity, such metrics must be sourced by exotic thin shells.

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arXiv2023

Shielding a charged black hole

We describe a shielding mechanism for a charged black hole immersed in a background involving charged matter fields, solely arising from the Einstein-Maxwell field equations. In particular, we consider a charged generalization of the Einstein cluster, that is a charged black hole surrounded by an effective fluid model for a partially charged dust cloud. We show that the shielding mechanism, arising thereof, is generic and appears in a different parametrization of the problem as well. In this process, we provide the most general electrovacuum solution in a spacetime region devoid of charges, but in the presence of a static and spherically symmetric charge distribution elsewhere. Side by side, we also introduce a convenient parametrization, providing the global solution of the Einstein-Maxwell's field equations in the presence of a charged black hole within the environment of charged fluid. We also comment on the nature of the photon sphere, shadow radius and the eikonal quasi-normal modes in the Einstein-Maxwell cluster.

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arXiv2022

Relativistic location algorithm in curved spacetime

In this article, we describe and numerically implement a method for relativistic location in slightly curved but otherwise generic spacetimes. For terrestrial positioning in the context of Global Navigation Satellite Systems, our algorithm incorporates gravitational as well as tropospheric and ionospheric effects modeled by the Gordon metric. The algorithm is implemented in the \textsc{squirrel.jl} code, which employs a quasi-Newton Broyden algorithm in conjunction with automatic differentiation of numerical geodesics. Our work provides a practical solution to the relativistic location problem in a generic spacetime and consolidates relativistic and atmospheric effects in a single framework. Though optimization is not our primary focus, our implementation is already fast enough for practical use, establishing a position from five emission points in $< 1~{\rm s}$ on a desktop computer for reasonably simple spacetime geometries. In vacuum, our implementation can achieve submillimeter accuracy considering the Kerr metric with terrestrial parameters and submeter accuracy including tropospheric and ionospheric effects.

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arXiv2022

Weiss variation for general boundaries

The Weiss variation of the Einstein-Hilbert action with an appropriate boundary term has been studied for general boundary surfaces; the boundary surfaces can be spacelike, timelike, or null. To achieve this we introduce an auxiliary reference connection and find that the resulting Weiss variation yields the Einstein equations as expected, with additional boundary contributions. Among these boundary contributions, we obtain the dynamical variable and the associated conjugate momentum, irrespective of the spacelike, timelike or, null nature of the boundary surface. We also arrive at the generally non-vanishing covariant generalization of the Einstein energy-momentum pseudotensor. We study this tensor in the Schwarzschild geometry and find that the pseudotensorial ambiguities translate into ambiguities in the choice of coordinates on the reference geometry. Moreover, we show that from the Weiss variation, one can formally derive a gravitational Schr{ö}dinger equation, which may, despite ambiguities in the definition of the Hamiltonian, be useful as a tool for studying the problem of time in quantum general relativity. Implications have been discussed.

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arXiv2022

Regularizing Dual-Frame Generalized Harmonic Gauge at Null Infinity

The dual-frame formalism leads to an approach to extend numerical relativity simulations in generalized harmonic gauge (GHG) all the way to null infinity. A major setback is that without care, even simple choices of initial data give rise to logarithmically divergent terms that would result in irregular variables and equations on the compactified domain, which would in turn prevent accurate numerical approximation. It has been shown, however, that a suitable choice of gauge and constraint addition can be used to prevent their appearance. Presently we give a first order symmetric hyperbolic reduction of general relativity in GHG on compactified hyperboloidal slices that exploits this knowledge and eradicates these log-terms at leading orders. Because of their effect on the asymptotic solution space, specific formally singular terms are systematically chosen to remain. Such formally singular terms have been successfully treated numerically in toy models and result in a formulation with the desirable property that unphysical radiation content near infinity is suppressed.

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arXiv2022

Peeling in Generalized Harmonic Gauge

It is shown that a large class of systems of non-linear wave equations, based on the good-bad-ugly model, admit formal solutions with polyhomogeneous expansions near null infinity. A particular set of variables is introduced which allows us to write the Einstein field equations in generalized harmonic gauge as a good-bad-ugly system and the functional form of the first few orders in such an expansion is found by applying the aforementioned result. Exploiting these formal expansions of the metric components, the peeling property of the Weyl tensor is revisited. The question addressed is whether or not the use of generalized harmonic gauge, by itself, causes a violation of peeling. Working in harmonic gauge, it is found that log-terms that prevent the Weyl tensor from peeling do appear. The impact of gauge source functions and constraint additions on the peeling property is then considered. Finally, the special interplay between gauge and constraint addition, as well as its influence on the asymptotic system and the decay of each of the metric components, is exploited to find a particular gauge which suppresses this specific type of log-term to arbitrarily high order.

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arXiv2022

Junction conditions and sharp gradients in generalized coupling theories

In this article, we develop the formalism for singular hypersurfaces and junction conditions in generalized coupling theories using a variational approach. We then employ this formalism to examine the behavior of sharp matter density gradients in generalized coupling theories. We find that such gradients do not necessarily lead to the pathologies present in other theories of gravity with auxiliary fields. A detailed example, based on a simple instance of a generalized coupling theory called the MEMe model, is also provided. In the static case, we show that sharp boundaries do not generate singularities in the dynamical frame despite the presence of an auxiliary field. Instead, in the case of a collapsing spherical density distribution with a general profile an additional force compresses over-densities and expands underdensities. These results can also be used to deduce additional constraints on the parameter of this model.

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arXiv2021

Self-collision of a portal wormhole

We consider the self-collision of portals in classical general relativity. Portals are wormholes supported by a single loop of negative mass cosmic string, and being wormholes, portals have a nontrivial topology. Portals can be constructed so that the curvature is zero everywhere outside the cosmic string, with vanishing ADM mass. The conical singularities of these wormholes can be smoothed, yielding a spatial topology of $S^2 \times S^1$ with a point corresponding to spatial infinity removed. If one attempts to collide the mouths of a smoothed portal to induce self-annihilation, one naively might think that a Euclidean topology is recovered, which would violate the classical no topology change theorems. We consider a particular limit of smoothed portals supported by an anisotropic fluid, and find that while the portal mouths do not experience an acceleration as they are brought close together, a curvature singularity forms in the limit that the separation distance vanishes. We find that in general relativity, the interaction between portal mouths is not primarily gravitational in nature, but depends critically on matter interactions.

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