> org.apache.solr.common.SolrException: Invalid Date
> String:'2011-01-07' at
> org.apache.solr.schema.DateField.parseMath(DateField.java:165)

Solr accepts date in the following format: 2011-01-07T00:00:00Z

> I understand from reading some articles that Solr stores
> time only in UTC,
> this is the query i am trying to index,

It seems that you are fetching data from a Relational Database. You may 
consider using http://wiki.apache.org/solr/DataImportHandler

> Why i am doing this timezone conversion is because i need
> to group results
> by the user timezone. How can i achieve this?

Save timezone info in a field and facet on that field?
http://wiki.apache.org/solr/SimpleFacetParameters

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