On a Gödel-like solution in non-relativistic gravity

{"Abstract":[0],"The":[1,149],"article":[2],"deals":[3],"with":[4],"Gödel-like":[5,61],"solutions":[6],"in":[7,110],"the":[8,36,46,66,94,101,105,159,164,169,199,206],"context":[9],"of":[10,16,82,163],"Galilean":[11,23,71],"gravity,":[12],"a":[13,21,32,60,70,75,80,153,204],"geometric":[14],"formulation":[15],"non-relativistic":[17,28,155],"gravitation":[18],"defined":[19],"on":[20],"five-dimensional":[22],"manifold.":[24],"Within":[25],"this":[26],"framework,":[27],"matter":[29,95],"fields":[30],"admit":[31],"covariant":[33],"description,":[34],"while":[35],"physical":[37],"Newtonian":[38],"dynamics":[39],"is":[40,91,97],"recovered":[41],"through":[42],"an":[43],"immersion":[44],"into":[45],"usual":[47],"$$3+1$$":[48],"<mml:math":[49,115,133,172],"xmlns:mml=\\"http://www.w3.org/1998/Math/MathML\\">":[50,116,134,173],"<mml:mrow>":[51,117,135,174,179,189],"<mml:mn>3</mml:mn>":[52],"<mml:mo>+</mml:mo>":[53],"<mml:mn>1</mml:mn>":[54,195],"</mml:mrow>":[55,128,146,183,193,196],"</mml:math>":[56,129,147,197],"spacetime.":[57],"By":[58],"adopting":[59],"metric":[62,106],"ansatz":[63],"and":[64,85,104,130,167,213],"coupling":[65],"gravitational":[67],"field":[68,87,102],"to":[69],"fluid":[72,165],"derived":[73],"from":[74],"variational":[76],"principle,":[77],"we":[78],"obtain":[79],"system":[81,90],"highly":[83],"nonlinear":[84],"coupled":[86],"equations.":[88],"This":[89],"solved":[92],"exactly:":[93],"sector":[96],"determined":[98],"algebraically":[99],"by":[100,158],"equations,":[103],"functions":[107],"are":[108],"obtained":[109],"closed":[111,215],"form,":[112],"$$D(x)=\\\\cosh":[113],"(mx)$$":[114,132],"<mml:mi>D</mml:mi>":[118,176],"<mml:mo>(</mml:mo>":[119,124,137,142,180,190],"<mml:mi>x</mml:mi>":[120,126,138,144,181,191],"<mml:mo>)</mml:mo>":[121,127,139,145,182,192],"<mml:mo>=</mml:mo>":[122,140,194],"<mml:mo>cosh</mml:mo>":[123],"<mml:mi>m</mml:mi>":[125,143],"$$H(x)=\\\\sinh":[131],"<mml:mi>H</mml:mi>":[136,186],"<mml:mo>sinh</mml:mo>":[141],".":[148],"resulting":[150],"configuration":[151],"describes":[152],"rotating":[154],"universe":[156],"supported":[157],"constant":[160],"potential":[161],"term":[162],"Lagrangian":[166],"satisfies":[168],"identity":[170],"$$D^{2}(x)-H^{2}(x)=1$$":[171],"<mml:msup>":[175,185],"<mml:mn>2</mml:mn>":[177,187],"</mml:msup>":[178,188],"<mml:mo>-</mml:mo>":[184],"throughout":[198],"entire":[200],"spatial":[201],"domain.":[202],"As":[203],"consequence,":[205],"associated":[207],"Killing":[208],"vector":[209],"remains":[210],"spacelike":[211],"everywhere":[212],"no":[214],"timelike":[216],"curves":[217],"arise.":[218]}

Authors

Institutions

Publication Details

Journal
The European Physical Journal Plus
Published
2026-07-29
DOI
https://doi.org/10.1140/epjp/s13360-026-08117-2
Primary Topic
Cosmology and Gravitation Theories
Type
article
Field-Weighted Citation Impact
0.00

Funders

Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
article

On a Gödel-like solution in non-relativistic gravity

S. C. Ulhoa, K. V. S. Araújo, R. G. G. Amorim, A. F. Santos
The European Physical Journal Plus
Cosmology and Gravitation Theories
article

On a Gödel-like solution in non-relativistic gravity

S. C. Ulhoa, K. V. S. Araújo, R. G. G. Amorim, A. F. Santos
article en

Abstract

Abstract The article deals with Gödel-like solutions in the context of Galilean gravity, a geometric formulation of non-relativistic gravitation defined on a five-dimensional Galilean manifold. Within this framework, non-relativistic matter fields admit a covariant description, while the physical Newtonian dynamics is recovered through an immersion into the usual $$3+1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> spacetime. By adopting a Gödel-like metric ansatz and coupling the gravitational field to a Galilean fluid derived from a variational principle, we obtain a system of highly nonlinear and coupled field equations. This system is solved exactly: the matter sector is determined algebraically by the field equations, and the metric functions are obtained in closed form, $$D(x)=\cosh (mx)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mo>cosh</mml:mo> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$H(x)=\sinh (mx)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mo>sinh</mml:mo> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . The resulting configuration describes a rotating non-relativistic universe supported by the constant potential term of the fluid Lagrangian and satisfies the identity $$D^{2}(x)-H^{2}(x)=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> throughout the entire spatial domain. As a consequence, the associated Killing vector remains spacelike everywhere and no closed timelike curves arise.

The European Physical Journal PlusVol. 141(7)
Universidade de Brasília (BR), Universidade Federal de Mato Grosso (BR), Canadian Quantum Research Center (CA)
Universidade de Brasília, Conselho Nacional de Desenvolvimento Científico e Tecnológico
Openalex Percentile: Top 10%
Cosmology and Gravitation Theories
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.